Yes. In all the states that explicitly provide for or mention a weapon permit/license as an acceptable form of voter identification, the permit includes a photographic component. On the other hand, many states have blanket clauses such as "any other government document that shows the elector's name and current address", which would presumably include a non-photographic weapon permit.
Arkansas Code § 7-1-101 requires that registration be verified by ID which includes a photographic component - subsection 39(C)iii. gives "A concealed handgun carry license" as an example of an ID that satisfies this requirement.
Florida Code §101.043 gives "A license to carry a concealed weapon or firearm" as valid ID, but the law states that it must include a picture.
Idaho Code §34-1113(5) allows for "A license to carry concealed weapons issued under section 18-3302, Idaho Code, or an enhanced license to carry concealed weapons issued under section 18-3302K, Idaho Code." Both of these licenses include a photo.
Kansas Code §25-2908h.(1)(C) gives "a concealed carry of handgun license issued by Kansas or a concealed carry of handgun or weapon license issued by another state or district of the United States" as valid ID, but prefaces the list of valid IDs with "The following forms of identification shall be valid if the identification contains the name and photograph of the voter and has not expired."
Mississippi Code §23-15-563 states that valid ID includes "A current and valid Mississippi license to carry a pistol or revolver", but prefaces this by requiring that all ID be "current and valid photo identification."
Texas Election Code Sec. 63.0101 states that "a license to carry a handgun issued to the person by the Department of Public Safety that has not expired or that expired no earlier than four years before the date of presentation" is valid photo ID, but makes no mention of weapons permits/licenses in the valid non-photo ID list.
Utah Code §20A-1-102 defines "Valid voter identification" as including "a currently valid Utah permit to carry a concealed weapon", but under the section headed "a form of identification that bears the name and photograph of the voter."
WV Code §3-1-34 considers "A valid concealed carry (pistol/revolver) permit issued by the sheriff of the county with a photograph of the person desiring to vote." to be a "valid identifying document".